The Role of Nonpolynomiality in Uniform Approximation by RBF Networks of Hankel Translates. (1st April 2019)

• Record Type: Journal Article
• Authors: Marrero, Isabel
• Other Names: Sawano Yoshihiro Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2019(2019)
• Publication Date: 2019-04-01
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2019/1845491
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : Givenμ > - 1 / 2 andc ∈ I = ] 0, ∞ [, let the spaceC μ, c (respectively, C μ ) consist of all those continuous functionsu on] 0, c ] (respectively, I ) such that the limitlim z → 0 + ⁡ z - μ - 1 / 2 u ( z ) exists and is finite;C μ, c is endowed with the uniform normu μ, ∞, c = sup z ∈ [ 0, c ] ⁡ z - μ - 1 / 2 u ( z ) ( u ∈ C μ, c ) . Assumeϕ ∈ C μ defines an absolutely regular Hankel-transformable distribution. Then, the linear span of dilates and Hankel translates ofϕ is dense inC μ, c for allc ∈ I if, and only if, ϕ ∉ π μ, whereπ μ = s p a n { t 2 n + μ + 1 / 2 : n ∈ Z + } .